Karzai, on a four-day US trip, is to visit the Arlington National Cemetery where many US soldiers killed in action in Afghanistan since the 2001 invasion are buried.
And at the Wednesday press conference he repeated a story he had already told to Secretary of State Hillary Clinton of an encounter with an American war veteran who is now a multiple amputee.
“It was a very difficult moment for me, Mr President … It was heart-rendering,” he told Obama.
Both leaders were anxious to assure the media that tensions that have existed since Obama took office and worsened since last year’s election have been exaggereated.
"There are going to be tensions in such a complicated, difficult environment and in a situation in which, on the ground, both Afghans and Americans are making enormous sacrifices," Obama said.
"With respect to perceived tensions between the US government and the Afghan government... a lot of them were simply overstated."
And Karzai was equally conciliatory.
"We are in a campaign against terrorism together, there are days that we are happy. There are days that we are not happy," he said.
Obama sought to reassure Karzai and the Afghan public that he takes civilian casualties at the hands of US-led troops seriously.
"Let me be very clear about what I told President Karzai. When there is a civilian casualty, that is not just a political problem for me," he said. "I am ultimately accountable... that is something that I have to carry with me... I don't want civilians killed."
And he claimed to see “progress” in efforts to fight corruption, with Karzai promising to “work with dedication and extreme care” in the management of foreign aid.
Obama also voiced support for Karzai's plan to win over Taliban defectors, although he added that they must renounce Al-Qaeda and violence.
On Friday Karzai will visit Fort Campbell, Kentucky, the headquarters of the US army’s 101st Airborne Division which will soon be deployed to Afghanistan.